Recall that
and the equation can be expressed as: \[\begin{align} y &= \beta x + c \\ \text{shift to Trump} & = \beta * \text{median income (\$1,000s)} + c. \end{align}\]
| % shift to Trump, 2012-2016 | |
| median income (1,000s) | -0.158*** |
| (0.006) | |
| Constant | 8.337*** |
| (0.351) | |
| Observations | 3,111 |
| Adjusted R2 | 0.203 |
| Note: | p<0.05; p<0.01; p<0.001 |
Each observation/data point is one county
Shift to Trump: How much more did the county vote for Trump in 2016 than it voted for Romney in 2012
median income ($1,000s): The county median income, expressed in units of $1,000. That is, a county with a $50,000 median income will be coded as 50. This is done to improve your ability to read the regression results.
% college experience: The percent of the county with at least some college experience, regardless of whether they earned a degree.
Recall that
and the equation can be expressed as: \[\begin{align} y &= \beta_1 x_1 + \beta_2 x_2 +c \\ \text{shift to Trump} & = \beta_1 * \text{median income (\$1,000s)} + \beta_2 * \text{% college experience} +c . \end{align}\]
| % shift to Trump, 2012-2016 | ||
| (1) | (2) | |
| median income (1,000s) | -0.158*** | -0.013 |
| (0.006) | (0.007) | |
| % college experience | -0.344*** | |
| (0.012) | ||
| Constant | 8.337*** | 20.103*** |
| (0.351) | (0.512) | |
| Observations | 3,111 | 3,111 |
| Adjusted R2 | 0.203 | 0.371 |
| Note: | p<0.05; p<0.01; p<0.001 | |
See https://drellaswat.github.io/trump_incomeedu_plane/ for a bigger version of this plot.
Adding in new variables, like education, controls for education. This means that each coefficient shows how much the outcome, shifting to Trump, changes as that variable changes, holding all other variables constant. This is called the marginal effect.
Example: A one unit change in county median income is associated with a -0.013 change in shifting to Trump when county education is held constant. You could imagine only looking at counties where around 40% of the county had attended college. Among those counties, a county with a median income of $50,000 is expected to shift to Trump 0.013% less than a county with a median income of $51,000. The same would be expected if we isolated to only counties with around 60% education.
Notice that the effect of income is much smaller when education is added to the equation.
Adding a new control/additional variable to a regression can change a coefficient’s value substantially when the new variable is strongly correlated with the original variable.
County income
County education